The aim of the present paper is to study a certain subclass of harmonic univalent functions with varying arguments defined by Salegean operator. For this class we determine a sufficient coefficient condition, representation theorem, distortion theorem, extreme points. Mathematics Subject Classification: Primary 30C45; Secondary 30C80

A comprehensive class of complex-valued harmonic prestarlike univalent functions is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Distortion bounds and extreme points are also obtained. 2000 Mathematics Subject Classification:Primary 30C45, 30C50.

Given two univalent harmonic mappings f1 and f2 on D, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f3 = (1−s)f1+sf2 to lift to a minimal surface for s ∈ [0, 1]. We then construct such mappings from Enneper’s surface to Scherk’s singularly periodic surface, Sckerk’s doubly periodic surface to the catenoid, and ...

A recent result of Sibel Yalcin et al. [4] appeared in “Journal of Inequalities in Pure and Applied Mathematics”(2007) concerning the convolution of two harmonic univalent functions in the class RSH (k, γ) is improved. 2010 Mathematics Subject Classification: 30C45.